Residual operations of monotone binary operations over complete lattices

被引：7
|
作者：
Sun, Feng [1 ]
Wang, Xue-ping [2 ]
Qu, Xiao-bing [1 ]
Shu, Qian-yu [2 ]
Zhang, Xiao-hong [3 ]
机构：
[1] Leshan Normal Univ, Coll Math & Informat Sci, Leshan 614000, Sichuan, Peoples R China
[2] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Sichuan, Peoples R China
[3] Shanghai Maritime Univ, Coll Arts & Sci, Dept Math, Shanghai 201306, Peoples R China
来源：
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2019年 / 110卷
基金：
中国国家自然科学基金;
关键词：
Monotone binary operations; Residual operations; Complete lattices; Distributivity; Implications; Coimplications; RIGHT SEMI-UNINORMS; CONTINUOUS T-NORMS; TRIANGULAR NORMS; PSEUDO-UNINORMS; R-IMPLICATIONS; COIMPLICATIONS; AGGREGATION; EQUATIONS; DISTRIBUTIVITY; OPERATORS;
D O I：
10.1016/j.ijar.2019.04.005
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
Various generalizations of triangular norms have been proposed, they are monotone binary operations satisfying commutativity or associativity or neutral property. Residual operations derived from these operations over complete lattices have been studied extensively. In this paper, residual operations of monotone binary operations over complete lattices are considered. Characterizations for these residual operations being implications or coimplications are given. Infinite distributivity, commutativity, associativity, neutral elements and annihilators of monotone binary operations and their residual operations are characterized. Finally, properties of residual operations derived from left (right) semi-uninorms, left (right) uninorms and (pseudo) uninorms are studied, and constructions of left (right) semi-uninorms, left (right) uninorms and (pseudo) uninorms through residuation are given. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：127 / 144
页数：18
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